<< A while ago someone posted a demonstration of the Lucas-Lehmer test
 for, I think, 2^7-1. >>

LL test:
S[0] = 4
S[k+1] = S[k] ^2 - 2  mod 2^P - 1
2^P - 1 is prime if and only if S[P-2] = 0.
Demonstration for 2^7 - 1 = 127:
S[0] = 4
S[1] = 4^2 - 2 mod 127 = 14
S[2] = 14^2 - 2 mod 127 = 194 mod 127 = 67
S[3] = 67^2 - 2 mod 127 = 4487 mod 127 = 42
S[4] = 42^2 - 2 mod 127 = 1762 mod 127 = 111
S[5] = 111^2 - 2 mod 127 = 12319 mod 127 = 0
S[7-2] = S[5] = 0, hence 2^7 - 1 is prime.

QED
YEA
STL
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